A262838 {3,7}-primes (defined in Comments).

2, 3, 23, 47, 53, 61, 67, 71, 89, 127, 137, 191, 397, 443, 701, 1031, 1117, 1223, 1499, 1549, 1579, 1621, 1699, 1933, 1951, 2129, 2207, 2311, 2381, 2473, 2521, 2671, 2731, 2753, 2833, 3011, 3019, 3061, 3967, 4051, 4093, 4127, 4229, 4397, 4457, 4943, 5023

Offset

1,1

Comments

Let S = {b(1), b(2), ..., b(k)}, where k > 1 and b(i) are distinct integers > 1 for j = 1..k. Call p an S-prime if the digits of p in base b(i) spell a prime in each of the bases b(j) in S, for i = 1..k. Equivalently, p is an S-prime if p is a strong-V prime (defined at A262729) for every permutation of the vector V = (b(1), b(2), ..., b(k)).

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Mathematica

{b1, b2} = {3, 7};
u = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &];  (* A231477 *)
v = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b2], b1]] &];  (* A262837 *)
w = Intersection[u, v]; (* A262838 *)
(* Peter J. C. Moses, Sep 27 2015 *)

Crossrefs

Cf. A000040, A231477, A262837, A262829.

Sequence in context: A090708 A359406 A199342 * A120366 A371310 A041787

Adjacent sequences: A262835 A262836 A262837 * A262839 A262840 A262841

Keyword

nonn,easy,base

Author

Clark Kimberling, Nov 09 2015

Status

approved